1) the form of the equation may be written as y = A(X - Xo)(X - X1)
Where Xo and X1 are the two roots of the equation.
2) We can fix the system of coordinates so that the vertex is in the middle of the gate => Xo = - 40 and X1 = +40
=> y = A (X + 40) (X - 40) = A (X^2 - 1600)
3) The height, at X = 0 is 25
=> A(0 - 1600) = 25
=> -1600A = 25 => A = -25 / 1600 = - 1/64
4) The equation is y = - [1/64] (X^2 - 1600)
5) You can present it in different equivalent forms.
Some of those other forms are:
1) - 64y = (x^2 - 1600)
2) x^2 = - 64y + 1600
3) X^2 = - 64 (y - 25)
Answer:
Step-by-step explanation:
n + q = 20
.05n + .25q = 3.00
5n + 25q = 300
n + q = 20
5n + 25q = 300
-5n - 5q = -100
20q = 200
q = 10 quarters
n + 10 = 20
n = 10 nickels
(10 nickels, 10 quarters)
Answer: IX - 4I ≤ 4
Step-by-step explanation:
In the numer line we can see that our possible values of x are in the range:
0 ≤ x ≤ 8
And we want to find an absolute value equation such that this set is the set of possible solutions.
An example can be:
IX - 4I ≤ 4
To construct this, we first find the midpoint M of our set, in this case is 4.
Then we write:
Ix - MI ≤ IMI
Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.
Answer:
y = 0
Step-by-step explanation:
Since there is no indication of a shift in the graph of f(x) = 3cos(-0.25x), then the midline must be the normal midline for a cosine or sine function which is: y = 0.
